In the 20th century, the molecular level of elucidation of biological molecules was developed. The quantum chemical understanding of the complex compounds has been developed with the development of quantum mechanics. Molecular biology, structural biology, and bioinorganic chemistry appeared, and we have come to understand many varieties of biological phenomena at the molecule and/or atomic levels, accompanied by the huge growth of computational science. The dawn of biomolecluar science occurred and its growth in the late of 19th–middle of 20th centuries is reviewed in this paper.

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The solutions (χ_nlm) of the Schrödinger equation for the hydrogen atom contain the term exp(imϕ). When m = 0, functions χ_nlm are real, however, in the cases of m ≠ 0, functions χ_nlm are complex. Probability density distribution of χ₃₂₀, χ_32±1, or χ_32±2 was sculptured in a glass block (Figure 1). Each picture is symmetric about the z axis. It was compared with 3-D isosurface model such as Figure 2. By taking linear combinations of χ₃₂₊₁ and χ₃₂₋₁, it is known to obtain the real atomic orbitals χ_3dzx and χ_3dyz. Similarly, from χ_32±2 and χ₃₂₋₂, the real atomic orbitals χ_3dx²-y² and χ_3dxy are obtained. In this paper, this mathematical process is graphically visualized (Figure 3). The "doughnut(s)" are sliced by plane(s) containing the z axis. The number of the plane(s) equals the |m| value. As the plane is a nodal plane, by rounding the edge and attaching positive or negative sign to each lobe, the familiar "clover" type orbital is obtained. Probability density distribution in the 3-dimensional representation of hydrogen four 3d orbitals thus obtained was sculptured in a glass block (Figure 4). Isosurface models (Figure 3, bottom) can hardly show the entire region where an electron can be found. On the other hand, in the diagram of probability density distribution models (Figure 4), an electron is found everywhere around the nucleus. Number of conical nodes together with planar nodes in hydrogen 3d atomic orbitals is summarized in Table 1.

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Geometries and potential energies for reactants of "H-Cl-Cl" around the transition state in the reaction of H + Cl₂ → HCl + Cl were calculated. The reactant on the transition state was formed at incident angle of 180°. This reactant was supported by the method of the intrinsic reaction coordinate (IRC). We produced a movie, which displays CGs of potential energy surfaces in 2-D and 3-D for reactants on the way of the reaction. The reaction profile with potential energy and structures of the reactants are also displayed. The profile was synchronized with the structures. The CG movie was tried, and it was improved through the application to student's learning on the Web. It was effective for students to acquire images of the reaction from the standpoint of its potential energy and molecular structure.

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Molecular modeling of the CAD system to create an STL file is almost non-existent. Molecular structure coordinate data, which have been published, cannot be directly exploited by CAD. OpenSCAD is written in an object language in the same way programmers write solid 3D CAD models. Therefore, molecular data in molecular modeling software (atom position x, y, z data) have been created. We are programming in OpenSCAD language to create an STL file.We have realized a series of programming work in molecular modeling software Winmostar (V6.003), and are running a version up of the OpenSCAD function. Without having to understand the OpenSCAD language, it is possible to create an STL file for the 3D printer of molecular models.

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Computational chemistry programs were evaluated as aids to teaching qualitative analytical chemistry. Computational chemical calculations can predict absorption spectra, thus enabling the modeling of indicator dissociation mechanisms by different computational chemical programs using a personal computer. An updated MNDO program among 51 programs was found to be the best predictor to explain the dissociation mechanisms of isobenzofuranones and sulfonephthaleins. Unknown dissociation constants were predicted from atomic partial charges instead of Hammett's constants.

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